Converting Odds Ratio to Relative Risk in Cohort Studies with Partial Data Information

Abstract

In medical and epidemiological studies, the odds ratio is a commonly applied measure to approximate the relative risk or risk ratio in cohort studies. It is well known tha such an approximation is poor and can generate misleading conclusions, if the incidence rate of a study outcome is not rare. However, there are times when the incidence rate is not directly available in the published work. Motivated by real applications, this paper presents methods to convert the odds ratio to the relative risk when published data offers limited information. Specifically, the proposed new methods can convert the odds ratio to the relative risk, if an odds ratio and/or a confidence interval as well as the sample sizes for the treatment and control group are available. In addition, the developed methods can be utilized to approximate the relative risk based on the adjusted odds ratio from logistic regression or other multiple regression models. In this regard, this paper extends a popular method by Zhang and Yu (1998) for converting odds ratios to risk ratios. The objective is novelly mapped into a constrained nonlinear optimization problem, which is solved with both a grid search and a nonlinear optimization algorithm. The methods are implemented in R package orsk which contains R functions and a Fortran subroutine for efficiency. The proposed methods and software are illustrated with real data applications.